Problem: Simplify the following expression: $k = \dfrac{-4n - 8}{2}$ You can assume $n \neq 0$.
Answer: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-4n - 8 = - (2\cdot2 \cdot n) - (2\cdot2\cdot2)$ The denominator can be factored: $2 = (2)$ The greatest common factor of all the terms is $2$ Factoring out $2$ gives us: $k = \dfrac{(2)(-2n - 4)}{(2)(1)}$ Dividing both the numerator and denominator by $2$ gives: $k = \dfrac{-2n - 4}{1}$ or more simply, $k = -2n - 4$